I'm not clear what you mean by a full purchase installation, as there is only one installer. You purchase when you subscribe or activate a subscription (or buy a retail copy and activate).
The first thing I'd recommend is using the McAfee cleanup utility to make sure it is completely gone from your PC.
McAfee Removal Tool - http://www.majorgeeks.com/McAfee_Consumer_Product_Removal_Tool_d5420.html
Then, if OneCare still won't start, see this post for a possible fix - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2523777&SiteID=2
MSMPENG.EXE is the antimalware engine used by OneCare and Defender. If it is using excessive CPU cycles, that would typically indicate a conflict with other active security software, so that may be resolved by running the McAfee removal tool.
If you continue to have problems, please contact support -
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
-steve